I had carried out simple test and 373 exported vertex colors correctly. And that UV sets issue is not present in 371, so that's one less thing to worry about in the workflow if you constantly create plenty of various meshes.
Ah, I may be mistaken there then. I know I've seen reports of issues with vertex colours, and I could've sworn I got mottled random vertex colours at one point when exporting with them. I haven't really needed vertex colours for the stuff I've done so far, so I've just been exporting without them and then switching 'has vertex colours' to yes in Nifskope (which sets vertex colour to white on all vertices).
Edit: Yep, Artisanix was right; I was able to export with vertex colours just fine, earlier (using 373).